C₅₉×#13693 #28425802

order	15104
nilpotency class	5
isoclinism	isoclinic class of #13691
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₉×#13693

Subgroups

	subgroup	G/H
center, socle	C₂×C₅₉	#2206
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₅₉
prime radical	C₅₉×#508	C₂²
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅₉ ◁ C₂×C₄×C₅₉ ◁ C₄×C₈×C₅₉ ◁ C₄×C₁₆×C₅₉ ◁ G

196 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 123
transitive degree	μ_t(G) = 3776

A minimal faithful permutation representation — 3 generators on 123 points:

(1,2,9,16)(3,14,20,35)(4,21,24,53)(5,15,8,12)(6,26,30,58)(7,10,19,36)(11,37,39,23)(13,41,44,28)(17,47,48,64)(18,40,50,43)(22,54,32,52)(25,34,29,57)(27,45,59,62)(31,42,51,63)(33,60,61,56)(38,55,46,49)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123);(1,3,8,19,9,20,5,7)(2,10,15,35,16,36,12,14)(4,17,32,51,24,48,22,31)(6,18,29,41,30,50,25,28)(11,33,46,62,39,61,38,45)(13,34,43,58,44,57,40,26)(21,42,54,64,53,63,52,47)(23,27,49,60,37,59,55,56);(1,4)(2,11)(3,17)(5,22)(6,27)(7,31)(8,32)(9,24)(10,33)(12,38)(13,42)(14,45)(15,46)(16,39)(18,49)(19,51)(20,48)(21,26)(23,28)(25,56)(29,60)(30,59)(34,54)(35,62)(36,61)(37,41)(40,47)(43,64)(44,63)(50,55)(52,57)(53,58)

Conjugacy classes & character table

2183 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 6681);